If B was (x, y) then B' is (-y, x).
It is (-6, -1).
(-1, -4) rotated 90 degrees anticlockwise
It is (-1, 6).Also, if the rotation is 180 degrees, then clockwise or anticlockwise are irrelevant.It is (-1, 6).
A rotation is a transformations when a figure is turned around a point called the point of rotation. The image has the same lengths and angle measures, and differs only in position. Rotations that are counterclockwise are rotations of positive angles. All rotations are assumed to be about the origin. R90 deg (x, y) = (-y, x) R180 deg (x, y) = (-x, -y) R270 deg (x, y) = (y, -x) R360 deg (x, y) = (x, y)
If you know how to rotate a triangle around the origin, treat the point as the origin.If you have Cartesian coordinates (that is x, y pairs) for the points of the triangle,subtract the coordinates of the centre of rotation from the coordinates of the triangle, do the rotation and then add them back on.Doing it geometrically:Draw line from centre of rotation to a point (for example a vertex)Measure the required angle from this line and draw in the rotated lineMeasure the distance from the centre of rotation to the original point and measure along the rotated line the required distance to get the rotated point.repeat for as many points as needed (eg the 3 vertices of the triangle) and join together the rotated points in the same was as the original points.[The construction lines drawn to the centre of rotation can be erased once the rotated point is found.]
A 180° rotation is half a rotation and it doesn't matter if it is clockwise of counter clockwise. When rotating 180° about the origin, the x-coordinate and y-coordinates change sign Thus (1, -6) → (-1, 6) after rotating 180° around the origin.
It is (-6, -1).
It is (-1, 6).
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
(-1, -4) rotated 90 degrees anticlockwise
The coords are (6, 1).
In two dimensions, the equations of rotation about the origin are: x' = x cos t - y sin t y' = x sin t + y cos t. where t is the angle of rotation, counterclockwise.
It is (-1, 6).Also, if the rotation is 180 degrees, then clockwise or anticlockwise are irrelevant.It is (-1, 6).
A rotation is a transformations when a figure is turned around a point called the point of rotation. The image has the same lengths and angle measures, and differs only in position. Rotations that are counterclockwise are rotations of positive angles. All rotations are assumed to be about the origin. R90 deg (x, y) = (-y, x) R180 deg (x, y) = (-x, -y) R270 deg (x, y) = (y, -x) R360 deg (x, y) = (x, y)
If you know how to rotate a triangle around the origin, treat the point as the origin.If you have Cartesian coordinates (that is x, y pairs) for the points of the triangle,subtract the coordinates of the centre of rotation from the coordinates of the triangle, do the rotation and then add them back on.Doing it geometrically:Draw line from centre of rotation to a point (for example a vertex)Measure the required angle from this line and draw in the rotated lineMeasure the distance from the centre of rotation to the original point and measure along the rotated line the required distance to get the rotated point.repeat for as many points as needed (eg the 3 vertices of the triangle) and join together the rotated points in the same was as the original points.[The construction lines drawn to the centre of rotation can be erased once the rotated point is found.]
Origin is at points (0, 0) in coordinate geometry. If you are shifting/translating the origin, you have to add the respective x and y coordinates of the new origin with respect to the old origin to get the coordinates of the new origin.
(0,0)